Constructs a rational k-gonal g-nodal canonical curve as follows:
Step 1. Computes a matrix s representing the canonical series of the singular curves with the function sectionsFromPoints from 2g points Pi,Qi.
Step 2. Computes the homogeneous ideal I of the curve as the kernel of the map s:T=kk[t0,...,tg-1]→S=kk[x0,x1].
The construction method is similar to the method implemented in the M2 package NodalCurves.
i1 : (k,g,n)=(4,8,1000); |
i2 : time (P,Q,multL,f)=pickGoodPoints(k,g,n);
-- used 0.131501 seconds
|
i3 : time I=idealOfNodalCurveByPoints(P,Q,n);
-- used 0.492393 seconds
ZZ
o3 : Ideal of ----[t , t , t , t , t , t , t , t ]
1009 0 1 2 3 4 5 6 7
|
i4 : time betti res I
-- used 2.62522 seconds
0 1 2 3 4 5 6
o4 = total: 1 15 39 50 39 15 1
0: 1 . . . . . .
1: . 15 35 25 4 . .
2: . . 4 25 35 15 .
3: . . . . . . 1
o4 : BettiTally
|